The new country would need to attract 20,000 more immigrants a year than presently expected in order to pay for pensions without raising taxes, The Scotland Institute said.

It said the Yes campaign had significantly underestimated the number of new entrants required to balance out the country's ageing population and provide the revenues to meet its promises.

Success in next week's referendum would pave the way for the introduction of a more "open-door policy".

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But the Institute said so many more were required that politicians in England and Wales - where immigration is a highly-contentious issue and demands are for tougher restrictions - could feel obliged to impose travel controls.

Institute executive chairman Azeem Ibrahim said: "Just how many immigrants we will need to come to Scotland every year from now till 2035 is a complicated issue with many variables.

"The calculations are dependent on what happens to North Sea oil revenues, the overall economic performance of Scotland, and changes to tax and benefits policies, among many others.

"But assuming all other things remain equal, we will need not a 2.5% but an 8% increase in the population of Scotland in the next two decades - or in other words, we need 20,000 more immigrants per annum than we are currently expecting.

He concluded: "Post-independence, Scotland can certainly aim to adjust this demographic deficit by advertising itself to global migrants. But pursuing an agenda of boosting immigration raises its own problems.

"England has a completely different demographic situation, and the political climate at Westminster is decidedly against increasing immigration.

"This means that an independent Scotland and the rest of the UK will find that they need hugely different immigration policies.

"And that raises the spectre of the unthinkable: the rest of the UK may not be able or willing to support a Common Travel Area policy with Scotland as currently exists between the UK and Ireland.

"And if that happens, we will see border guards along Hadrian's Wall before too long. That is unthinkable. But it may well end up being politically inevitable in case Scotland becomes independent."

Scottish Conservative finance spokesman Gavin Brown said: "Once again, we are left with the distinct impression that Alex Salmond is simply pulling out figures from thin air, based on nothing but assertion.

"The First Minister says immigration will raise an extra £1.5 billion a year but can't produce the workings to back up his numbers.

"Projecting our future population is crucial to planning and paying for public services and pensions.

"But, the truth is that the SNP's financial case for independence is pure fantasy."